Gaussian Measure of Large Balls in $l_p$
Linde, Werner
Ann. Probab., Tome 19 (1991) no. 4, p. 1264-1279 / Harvested from Project Euclid
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We study the behaviour of $\mu\{x \in E; \|x\| > t\}$ as $t \rightarrow \infty$ for a Gaussian measure $\mu$ in a Banach or quasi-Banach space in the following cases: 1. $E = l_p, 2 < p < \infty$, and $\mu$ of diagonal form but not necessarily symmetric; 2. $E =$ Hilbert space and $\mu$ arbitrary; 3. $E = l^n_p, 0 < p < 2$, and $\mu$ of diagonal form. While 2 solves a problem of Hweng (1980), 1 and 3 extend some results of Dobric, Marcus and Weber (1988).
Publié le : 1991-07-14
Classification:  Gaussian measure,  tail behaviour,  $l_p$-space,  60B11,  60G15,  60F10 
@article{1176990343,
     author = {Linde, Werner},
     title = {Gaussian Measure of Large Balls in $l\_p$},
     journal = {Ann. Probab.},
     volume = {19},
     number = {4},
     year = {1991},
     pages = { 1264-1279},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176990343}
}

Linde, Werner. Gaussian Measure of Large Balls in $l_p$. Ann. Probab., Tome 19 (1991) no. 4, pp.  1264-1279. http://gdmltest.u-ga.fr/item/1176990343/